The cross section for the proton weak capture reaction H-1(p,e(+) nu(e
))H-2 is calculated with wave functions obtained from a number of mode
rn, realistic high-precision interactions. To minimize the uncertainty
in the axial two-body current operator, its matrix element has been a
djusted to reproduce the measured Gamow-Teller matrix element of triti
um p decay in model calculations using trinucleon wave functions from
these interactions. A thorough analysis of the ambiguities that this p
rocedure introduces in evaluating the two-body current contribution to
the pp capture is given. Its inherent model dependence is in fact fou
nd to be very weak. The overlap integral Lambda(2)(E = 0) for the pp c
apture is predicted to be in the range 7.05-7.06, including the axial
two-body current contribution, for all interactions considered.